the map \(\operatorname{Spec}\mathbb {F}_{\mathfrak {p}}\hookrightarrow \operatorname{Spec} \mathcal {O}_{\mathfrak {p}}\)  is induced by reduction mod-\(\mathfrak {p}\)  and is an étale homotopy equivalence (see [1]}). On the other hand, the map \(\operatorname{Spec} K_{\mathfrak {p}} \hookrightarrow \operatorname{Spec} \mathcal {O}_{\mathfrak {p}}\)  is induced by the inclusion of \(\mathcal {O}_{\mathfrak {p}}\)  in \(K_{\mathfrak {p}}\) .
